Common Maths Lesson - Enlargement and Reducement

Common Maths-English Lesson - Pythagorean Cup

There is an odd bump in the center of the cup, but otherwise, it seems quite normal, and if it is filled to a certain level can be used without
incident.

However, if the cup is filled higher than the bump, the drink starts to drain out of the bottom — in fact, the cup will completely empty
itself!

This is the trick of the Pythagorus cup, also known as the Pythagorean cup or the Tantalus cup!

MATERIALS FOR LESSON "PYTHAGOREAN CUP"

Open Lesson for students and teachers - Programming language- Scratch

Open Lesson- workshop for students and teachers from Poland, Italy and Greece.

ICT Teacher - Lia - Greece

Scratch is a programming language that makes it easy to create your own interactive stories, animations, games, music, and art -- and share your creations on
the web.

As young people create and share Scratch projects, they learn important mathematical and computational ideas, while also learning to think creatively, reason
systematically, and work collaboratively.Scratch can be used in many different settings: schools, museums, community centers, and homes. It is intended especially for 8- to 16-year-olds, but
younger children can work on Scratch projects with their parents and college students use Scratch in some introductory computer science classes.

Workshop for students in Foundation of the Hellenic Word in Athens

Exhibition : Dvelopment of Mathematics and Mathematical Thought in the Ancient Greek World

We viewed very interesting Exhibition. That was fantastic journey to the world of Greek mathematics.

The exhibition dealt with the development of mathematics and mathematical thought in the ancient Greek world. Through the use of new technologies (video,
digital interactive applications, Virtual Reality exhibits) and the adoption of modern museological conceptions, the exhibition attempted to demonstrate the importance of ancient Greek
mathematics for Hellenic and European culture. Our tour started from the 6th century BC and culminated in the 4th century AD, examining all the significant "events" and people in
the history of Greek mathematics. There was a brief reference to pre-Hellenic mathematics of the Egyptians and the Babylonians, as well as to the course of the texts of Greek mathematicians
after the end of the ancient world, from the Byzantine monasteries and the Arab copying workshops to the European Renaissance scientists and the period of Scientific Revolution. The
presentation of scientific applications in astronomy, mathematical geography and music created a more complete image of ancient Greek mathematics.

I Section

The main part of the first section wasvthe tour of the culture and mathematics of the people of Egypt and Mesopotamia during the 2nd and 1st millennia BC. A
series of activities revealed to us the arithmetical and computational systems of these two cultures.

II Section

Interactive exhibits, digital and mechanical, images, texts and videos unraveled the first period of development of Greek
mathematics in the 6th and 5th centuries BC. That was the period of Thales and the Ionian philosophers, of Pythagoras and the Pythagoreans in southern Italy. The earliest mathematical expressions
were formulated in an effort to describe observations made about the qualities of shapes and numbers. Mathematics was still closely related to philosophy.

Section III

The second half of the 5th and 4th centuries BC. This is the period of Plato, Euclid and Aristotle, the age of Classical Athens.

Various types of exhibit bring to life the way in which the concept of mathematical proof was born, during this second period of the history of Greek
mathematics. Mathematical proof was of paramount importance to the development of the science of mathematics.

Section IV

Here we found ourselves in the Hellenistic Period, when Alexandria was the centre of developments.

In this unit, we have been impressed to learn how mathematics flourished after the discovery of mathematical proof. The heyday of Greek mathematics and
the formulation of methods and theories is presented with both digital and more traditional means, while the unit also demonstrates the work of three of the greatest mathematicians of Antiquity,
Apollonius, Archimedes and Eratosthenes.

Section V

While Greek mathematics developed apace, many other scientific fields that were based on it grew rapidly alongside.

Subjects such as music and mathematical geography was presented in independent units of the exhibition. However, this section presented astronomy in all its
diachronic character, with information about the first astronomical observations and the creation of the first calendars, and also the ingenious mathematical models that were invented to describe
the movement of the planets.

Section VI

This section was diachronic like the previous one. We came into contact here with many of the applications of mathematics to various fields of
everyday life.

Which instruments are used to measure the height of a tree?

How can we calculate the number of eggs in the old womans basket, taking into consideration that they are all broken and she does not remember how many they
were?

The answers were all here!

Section VII

This section formed the epilogue of the exhibition. It describes how ancient Greek mathematical manuscripts travelled from Byzantium and the Arab world to
their final destination in Western Europe, which eventually led to the scientific revolution. Many European mathematicians, from the 16th century onwards, are introduced here, as are their
achievements.

We visited also the "Tholos" - Foundation's new dome-shaped Virtual Reality "Theatre". It is a building of exceptional architectural design and
with unique technological infrastructure, which hosts FHW's digital collections.

The "Tholos" resembles a planetarium regarding its natural and morphological characteristics. However, their only common characteristic is the semi-circular
shape of the projection surface. The exterior shape of the "Tholos" refers to a whirling celestial body. It a sensation that is rendered through the processing of surfaces and the selection of
materials, such as the successive rings that surround the external shell and the special lights that make it stand out during the night. Thus, the "Tholos" becomes a symbol of Hellenism and
characterizes Pireos street.

The shows was interactive, controlled by the spectator, and not static. It was a unique experience of immersion into the virtual world, which is
characterized by immediate response, flexibility, originality and liveliness. That was fantastic experience for students and teachers.